Question: Solve for $x$ and $y$ using elimination. ${-4x+y = -11}$ ${5x-4y = 11}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ ${-16x+4y = -44}$ $5x-4y = 11$ Add the top and bottom equations together. $-11x = -33$ $\dfrac{-11x}{{-11}} = \dfrac{-33}{{-11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-4x+y = -11}\thinspace$ to find $y$ ${-4}{(3)}{ + y = -11}$ $-12+y = -11$ $-12{+12} + y = -11{+12}$ ${y = 1}$ You can also plug ${x = 3}$ into $\thinspace {5x-4y = 11}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ - 4y = 11}$ ${y = 1}$